To determine the probability of getting exactly 2 tails when flipping a fair coin 7 times, we can make use of the binomial probability formula. This formula is particularly applicable because we have a fixed number of trials (7 flips), two possible outcomes (heads or tails), and each flip of the coin has the same … Read more
An exponent is a fundamental concept in mathematics that indicates how many times a number, known as the base, is multiplied by itself. For example, in the expression 23, the number 2 is the base, and the exponent is 3. This means that you multiply the base (2) by itself three times: 2 × 2 … Read more
To determine what constant should be added to the expression x² + 6x in order to form a perfect square trinomial, we can follow a systematic approach. A perfect square trinomial can be expressed in the form (a + b)², which expands to a² + 2ab + b². In our case, we need to rewrite … Read more
To multiply and simplify the expression involving the numbers 3, 5i, 2, and 4i, you can follow these steps: Group the terms: Start by rearranging the expression for clarity: (3 * 2) * (5i * 4i) Multiply the real numbers: First, multiply the real components: 3 * 2 = 6 Multiply the imaginary numbers: Next, … Read more
To find the nth term of the sequence given (1, 4, 7, 10), we need to identify the pattern or rule that describes the relationship between the terms in the sequence. Looking at the sequence, we see: The first term (n=1) is 1 The second term (n=2) is 4 The third term (n=3) is 7 … Read more
Graphing a Set on the Number Line Graphing a set on a number line is a straightforward process. To illustrate this, let’s assume our set is S = {x | -3 < x < 2}. Here’s how you can effectively graph this set: Draw a Horizontal Line: Begin by drawing a straight horizontal line, which … Read more
In vector mathematics, the component of vector a along the direction of vector b can be determined using the concept of projection. The projection of vector a onto vector b essentially tells us how much of a points in the direction of b. The formula for the projection of vector a onto vector b is … Read more
To solve for t in the equation 32t – 5 = 5t + 25, we will follow these steps: Isolate the variable terms on one side: First, we can move the 5t term from the right side to the left side. To do this, we subtract 5t from both sides: 32t – 5 – 5t … Read more
Geometric Shapes: Edges, Faces, and Vertices Understanding the fundamental properties of geometric shapes is essential for students and enthusiasts alike. Below, we outline the number of edges, faces, and vertices associated with each of the following shapes: 1. Cube Edges: 12 Faces: 6 Vertices: 8 2. Cuboid Edges: 12 Faces: 6 Vertices: 8 3. Cone … Read more
A parallelogram is a special type of quadrilateral where opposite angles are equal, and the sum of adjacent angles is supplementary, meaning they add up to 180 degrees. Given that one angle measures 80 degrees, we can determine the measures of the remaining angles as follows: The angle opposite to the 80-degree angle is equal … Read more